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Chapter 12 Postulates & Theorems
Standard Equation of a Circle
The standard equation of a circle with center (h,k) and radius r is (x-h)²+(y-k)²=r²
Arc Addition Postulate
The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs
In a plane, a line is tangent to a circle IFF
the line is perpendicular to a radius of the circle at its endpoint on the circle
Tangent segments from a common external point are
In the same circle, or in congruent circles, two minor arcs are congruent IFF
their corresponding chords are congruent
If one chord is the perpendicular bisector of another chord
then the first chord is a diameter
If a diameter of a circle is perpendicular to chord,
then the diameter bisects the chord and its arc
In the same circle, or in congruent circles, two chords are congruent IFF
they are equidistant from the center
Measure of an Inscribed Angle Theorem
The measure of an inscribed angle is one half the measure of its intercepted arc
If two inscribed angles of a circle intercept the same arc,
then the angles are congruent
An angle inscribed in a semicircle
is a right angle.
The opposite sides of a quadrilateral inscribed in a circle are
If a tangent and a chord intersect at a point on a circle,
then the measure of each angle formed is one half the measure of its intercepted arc